|Publication number||US7734525 B2|
|Application number||US 11/527,324|
|Publication date||Jun 8, 2010|
|Filing date||Sep 26, 2006|
|Priority date||Sep 27, 2005|
|Also published as||EP1934919A2, EP1934919A4, US8924275, US20070208649, US20100223204, WO2007038477A2, WO2007038477A3|
|Publication number||11527324, 527324, US 7734525 B2, US 7734525B2, US-B2-7734525, US7734525 B2, US7734525B2|
|Inventors||Mikhail Zborovskiy, Dimitri Turchin|
|Original Assignee||Morgan Stanley|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (7), Non-Patent Citations (2), Referenced by (14), Classifications (12), Legal Events (2)|
|External Links: USPTO, USPTO Assignment, Espacenet|
This application claims priority from the U.S. Provisional Patent Application Ser. No. 60/721,239 filed on Sep. 27, 2005, the disclosure of which is incorporated herein by reference.
The present invention is directed generally and in various embodiments to computer simulation systems and methods, and more particularly, to hybrid multi-thread and multi-process computer simulation systems and methods for pricing trades in an investment portfolio in order to determine credit exposure.
The general problem addressed by this application is as follows. A computer system is required to obtain solutions to a very large number of independent problems and then generate a comprehensive result based on the solutions. The individual problems may be of widely-differing complexity and may thus demand widely-differing amounts of computational time to solve. Although solving the problems may depend upon one or more common inputs, the problems are independent in that each may be solved without reference to the solution obtained for any of the others. As used herein, the term “problem module” refers to each of the independent problems.
The specific problem addressed by this application is that of evaluating credit exposure associated with an investment portfolio. In particular, it is frequently necessary for investment portfolio owners to quantify their credit exposure to each counterparty within a given investment portfolio. The portfolio typically comprises a collection of counterparties, with each counterparty obligated to make payments to the portfolio owner and/or perform other duties in accordance with one or more financial instrument transactions, referred to herein as “trades”. The financial instruments underlying each transaction may be, for example, derivative instruments such as call or put options having a value dependent upon some financial asset, commodity index, predefined variable, or a combination thereof. The total credit exposure of the portfolio owner to each counterparty may be represented as a sum of a current exposure and a potential exposure. The current exposure represents the maximum loss that the portfolio owner would incur if the counterparty would currently fail to perform its obligations (i.e., default). The potential exposure represents the maximum loss that would be incurred if the counterparty would default at a future date prior to the maturity of the instrument. Credit exposure determinations by the portfolio owner may be used for, among other things, approving additional transactions with a counterparty based upon a predetermined credit limit for that counterparty and for credit risk valuation.
Because a determination of potential exposure is inherently speculative, statistical models are frequently employed for simulating a portfolio owner's potential exposure to each counterparty within a given portfolio. As a first step, such models typically simulate a large number of market scenarios based upon, among other things, one or more market risk factors affecting values of trades associated with each counterparty. Such risk factors may include, for example, future prices of traded assets, interest rates, and currency exchange rates. Each market scenario may, for example, provide numerical values for such factors at a plurality of time horizons, for example, each month for a specified period of time. Each scenario may also include a probability representing the likelihood of its occurrence.
The time over which the market scenarios are simulated may be selected based upon the time remaining until the maturity of financial instruments underlying the trades. Creation of simulated market scenarios may be implemented, for example, using known Monte Carlo simulation techniques. Upon creation of the simulated market scenarios, each trade associated with a particular counterparty may be priced over the time horizons for each simulated market scenario. Based upon the determined pricings, the portfolio owner's potential exposure to the counterparty with respect to each simulated market scenario may be determined. The potential exposures for all of the simulated market scenarios may then be statistically analyzed in order to determine an overall estimate of portfolio owner's potential exposure to the counterparty. If necessary, the estimated potential exposures of counterparties within a portfolio may be combined to determine an estimate of the potential exposure represented by the entire portfolio.
The process of pricing trades in order to determine an estimate of a portfolio owner's credit exposure to each counterparty within a portfolio is computationally intensive. In particular, large investment portfolios routinely comprise tens of thousands of counterparties, with each counterparty contractually obligated to the portfolio owner under one or more transactions. Where a large number of market scenarios (e.g., 1000-2000) is created, as well as a substantial number of time horizons for the scenarios, the number of pricing computations necessary may easily be on the order of tens of billions. The ability of the portfolio owner to make real-time investment decisions based upon credit exposure is thus generally limited by the amount of time required to perform such pricing computations.
The determination of credit exposure is an example of the general problem cited above. In particular, the problem modules cited for the general problem correspond to the calculation of credit exposure for the individual trades associated with a particular counterparty. The determination of credit exposure falls within the scope of the general problem because the credit exposure for each individual trade may be calculated without reference to the credit exposure for any other trade. Because the complexity of trades typically varies widely in scope, calculating credit exposure for the individual trades generally requires widely-differing amounts of computational time.
Pricing trades for determining a portfolio owner's potential exposure has historically been performed using a multi-threaded process approach.
The time required for each multi-threaded process 20 to price the trades 40 for a given counterparty 45 is largely determined by the number and complexity of the trades 40. In particular, whereas certain of the trades 40 may be simple and thus priced relatively quickly, other trades 40 may be more complex and require significantly more time for pricing. Each trade 40 may have associated with it an algorithm that is to be run for each of the market scenarios over each of the time horizons. The type of trade 40 determines the complexity of the algorithm and the time required for it to run.
Computer systems utilizing purely multi-threaded processes for pricing counterparty trades 40, such as that of
In one general respect, this application discloses a method for performing a calculation that includes determining solutions for a plurality of problem modules. The problem modules are of differing complexities, and their solutions are combined to determine a solution to the calculation. The method may include directing each of the problem modules to at least one master server, estimating a complexity for each of the problem modules, determining a threshold complexity level, sending problem modules having a complexity exceeding the threshold complexity level to at least one slave server and obtaining solutions for the problem modules therefrom, determining solutions for problem modules having a complexity not exceeding the threshold complexity level in the master server(s), and combining the solutions for the problem modules to determine the solution for the calculation.
In another general respect, this application further discloses a method for quantifying the credit exposure of an investment portfolio owner to a counterparty within the investment portfolio, the counterparty being obligated to the portfolio owner in accordance with a plurality of trades. The method may include sending signals indicative of the counterparty and the trades to at least one master server, estimating a complexity for each of the trades, determining a threshold complexity level, determining a price for each of the trades having a complexity not exceeding the threshold complexity level in the master server(s), sending each trade having a complexity exceeding the threshold complexity level to at least one slave server and determining a price for the trades in the slave server(s), and combining the prices for the trades to determine the credit exposure of the portfolio owner to the counterparty.
In another general respect, this application discloses a method for calculating a base complexity of trade pricing algorithms based on a plurality of scenarios. The scenarios represent future values of parameters relevant to the prices of the trades over a plurality of time horizons. Each base complexity pertains to a specific trade type and is used for estimating actual trade complexity. The method includes, for each trade type, defining a test trade embodying at least one characteristic feature of the trade type, pricing the test trade based on a plurality of the scenarios, and determining the base complexity for the trade type based on the time required to price the test trade on the plurality of scenarios.
As shown in
The above-described approach also facilitates the estimation of relative complexities for trades of different product types. In particular, a canonical-form complexity component may be introduced for every product type and encoded with the relative adjustment of a real trade with respect to the canonical form. While choice of the canonical form for each product type can be arbitrary, it is important to accurately capture actual trade complexity with respect to the canonical form. Canonical-form complexity may then be estimated empirically by running repeated computations of the canonical forms of all product types in a controlled environment and determining the computational time required for each canonical form. The number of repeated computations can be different for different product types since the time required per computation factors out. In effect, canonical-form complexity synchronizes the computation of different products. It should be noted that the measure of complexity need not be expressed in real time units (e.g., milliseconds, years), and any complexity measure that suitably represents the relative complexities of trades may be used. For example, estimated complexities of trade A and trade B may be represented by numbers 100,000 and 200,000, respectively, which are unitless and do not represent real time. Nonetheless, because the estimated complexity of trade B is twice that of trade A, it will be understood that pricing trade B will take twice as long as pricing trade A.
Complexity of a single trade computation may thus depend on an empirically-estimated canonical form, or “initial,” complexity component, and an actual-to-canonical adjustment of the initial complexity component based on actual trade facts. It should be noted that the product of these components may not yield overall trade complexity, and in certain cases (as described in connection with examples set forth below) the complexity adjustment with respect to the canonical form may be non-linear.
Complexity of a single trade computation may additionally or alternatively depend on factors in addition to the empirically-estimated canonical-form complexity component and the actual-to-canonical adjustment. In certain embodiments, for example, the minimal unit of work may be computation along a single path for all time horizons, and as a trade approaches maturity, the time required to compute price may decrease. After the trade matures, it may no longer contribute to exposure, in which case price computations for the trade may no longer be necessary. Accordingly, a third component of complexity may be an adjustment to the actual time horizons required by the computation. In some cases (e.g., a vanilla option), pricing may be invariant with respect to time to maturity, and the third component may only require computing the number of time horizons before trade maturity.
To summarize, three components may be used to determine trade complexity: (1) a canonical-form complexity component, estimated empirically; (2) an actual-to-canonical adjustment component, encoded based on pricing algorithm analysis; and (3) a time horizon adjustment component, encoded based on analysis of pricing algorithm and the actual time horizons over which the computations will be performed. The following examples illustrate determinations of complexity for different types of products.
The dollar value of a “single payment” trade was defined as the product of the notional amount, the discount factor and the currency exchange rate. A payment of
The value of a “floating leg” trade is the sum of the discounted future cash flows, defined as the product of the notional amount, the appropriate forward rate and the accrual period. The overall time needed to compute this trade is linear with respect to the number of future cash flows, but invariant with respect to other parameters (e.g., notional amount, currency, rates). The number of remaining cash flows is determined by the time to maturity and the frequency of payments—parameters which are part of, or can be easily inferred from, the trade description. A one-year
For “basket default swap” trades, pricing efficiency may be increased by using two different approximation methods based on basket size. In this example, for large baskets (e.g., >20 obligors), a pricing methodology based on the Central Limit Theorem (CLT) was used. For small baskets (e.g., ≦20 obligors), a pricing methodology based on the Probability Generating Function (PGF) was used. Each methodology is non-linearly dependent on the number of obligors, but linearly-dependent on the number of premium payments. Instead of computing an initial complexity for a canonical form and subsequently computing an actual-to-canonical adjustment, a “combined” complexity estimate was estimated. The complexity of a basket computed using the PGF methodology was exponential in form (in terms of the number of obligors), and the complexity of a basket computed using the CLT methodology was represented as a second-degree polynomial. To estimate the coefficients of these formulae, a single cash flow basket was chosen and a number of pricing computations were performed using 5, 10, 15 and 20 obligors for the PGF methodology, and 20, 35, 50, 70, 100 and 150 obligors for the CLT methodology. The number of obligors was then fitted to observed CPU times using the functional forms above to yield the following equations: (wherein the number of obligors is denoted by x):
Initial complexity (CLT)=20.399*x 2+249.61*x−1957.2
Initial complexity (PGF)=484.84*x 3.04
The actual-to-canonical adjustment is defined to be a multiplier equal to the number of cash flows of the actual trade. The time-horizon adjustment requires iterating over the time horizons and summing the number of remaining cash flows determined by the maturity and frequency of the trade.
As shown in
The multi-threaded process 60 may next be initiated on each master server 55 in accordance with the output provided by the root script 75 of the control server 76. As shown in
For each trade 65 having a complexity greater than or equal to the defined complexity threshold 85, the corresponding master server 55 may initiate a separate process within one of the one or more slave server pools 80 in communication therewith. The master server 55 may then serialize data relating to each of these trades 65, as well as data relating to the simulated market scenarios, for distribution to the corresponding processes within the one or more slave server pools 80. Based upon the received serialized data, each process within the slave server pools 80 may then price the trade 65 utilizing a process thread (not shown) implemented within a corresponding slave server engine 100 of a slave server. Thus, for trades 65 of greater complexity, pricing computations are parallelized utilizing a distributed multi-process approach. Pricings generated by processes implemented within the slave server pools 80 may be serialized, communicated to the corresponding master server 55, and aggregated with pricings determined locally within the master server 55.
It will thus be appreciated that the computer system 50 of
In step 150, the complexity of each problem module is compared with the threshold complexity level 85. Those problem modules having a complexity not exceeding the threshold complexity level 85 are processed in the master server 55 in step 160, while those problem modules having a complexity exceeding the threshold complexity level 85 are sent to a slave server engine 100 within a slave server pool 80 in communication with the master server 55 for processing.
In step 180, solutions for all the problem modules are combined to determine a solution for the composite problem 105.
In step 150, the complexity of the problem modules is compared with the threshold complexity level 85. Those problem modules having a complexity not exceeding the threshold complexity level 85 are processed in the master server 55 in step 160, while those problem modules having a complexity exceeding the threshold complexity level 85 are tested in step 220. Those problem modules having exceptionally great complexity may be, in step 240, distributed to a plurality of slave server engines 100 for processing. Each problem module not having exceptionally great complexity may be solved in a single slave server engine 100 in step 170. In step 180, the solutions for all the problem modules may be combined to determine a solution for the composite problem. It is noted that step 210, wherein the problem modules are sorted, and step 240 wherein exceptionally complex problem modules are solved in a plurality of slave server engines 100, may be employed independently of each other, or in the same process 200.
A party practicing method 300 is considered to have a database including a large number of scenarios, each scenario specifying values for a large number of economic indicators over a plurality of time horizons. The time horizons may, for example, be each month for a specified time period. Each trade 65 is priced by applying a pricing algorithm to the trade 65 using the scenarios as data.
In step 310, each trade 65 is directed to one of a plurality of master servers 55. In step 320, the complexity of each trade 65 is estimated. In step 330, a threshold complexity level 85 is determined. In step 340, the complexity of each trade 65 is compared with the threshold complexity level 85. If the estimated complexity for a particular trade 65 does not exceed the threshold complexity level 85, the price of the trade 65 is calculated in step 350 in the master server 55. If the complexity of the trade 65 exceeds the threshold complexity level 85, then, in step 360, the trade 65 is priced in one of the slave server engines 100 of the slave server pool 80. In step 370, the prices of all the trades 65 are combined to determine the portfolio owner's credit exposure to the counterparty 70.
As in method 300, method 400 further includes step 330 to determine a threshold complexity level 85, and each trade 65 is tested in step 340 to determine whether its complexity exceeds the threshold complexity level 85. If the complexity of a trade 65 does not exceed the threshold complexity level 85, then its price is determined in step 350 in master server 55. If its price exceeds the threshold complexity level 85, then it is tested again in optional step 420 to determine whether it has exceptionally great complexity. If it does not have exceptionally great complexity, then its value is determined in step 360 in one of the slave server engines 100 of the slave computer pool 80. If it does have exceptionally great complexity, then, in step 430, it is distributed to a plurality of slave server engines 100 in the slave computer pool 80 for processing. For example, one group of scenarios for the trade 65 may be processed in one slave server engine 100 and another group in a different slave server engine 100. In step 370, prices for all the trades 65 are combined to determine the portfolio owner's credit exposure to the counterparty 70.
The actual estimated complexity of a particular trade type is the base complexity modified by the actual facts of the trade 65, and the number of time horizons over which it is to be evaluated.
As used herein, a “server” may be, for example and without limitation, either alone or in combination, a personal computer (PC), main frame, microcomputer, minicomputer, laptop, personal data, processor, including wireless and/or wireline varieties thereof, and/or any other computerized device capable of configuration for processing data for standalone application and/or over a networked medium or media. Servers disclosed herein may include operatively associated memory for storing certain software applications used in obtaining, processing, storing and/or communicating data. It can be appreciated that such memory can be internal, external, remote or local with respect to its operatively associated computer or computer system. Memory may also include any means for storing software or other instructions including, for example and without limitation, a hard disk, an optical disk, floppy disk, ROM (read only memory), RAM (random access memory), PROM (programmable ROM), EEPROM (extended erasable PROM), and/or other like computer-readable media.
Servers disclosed herein may operate according to software code to be executed by a processor or processors of the server or any other computer system using any type of suitable computer instruction type. The software code may be stored as a series of instructions or commands on a computer readable medium. The term “computer-readable medium” as used herein may include, for example, magnetic and optical memory devices such as diskettes, compact discs of both read-only and writeable varieties, optical disk drives, and hard disk drives. A computer-readable medium may also include memory storage that can be physical, virtual, permanent, temporary, semi-permanent and/or semi-temporary. A computer-readable medium may further include one or more data signals transmitted on one or more carrier waves.
While several embodiments of the invention have been described, it should be apparent, however, that various modifications, alterations and adaptations to those embodiments may occur to persons skilled in the art with the attainment of some or all of the advantages of the disclosed invention. Therefore, this application is intended to cover all such modifications, alterations and adaptations without departing from the scope and spirit of the disclosed invention as defined by the appended claims.
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|U.S. Classification||705/36.00R, 705/35, 705/37|
|Cooperative Classification||G06Q40/04, G06Q40/00, G06F9/505, G06Q40/06|
|European Classification||G06F9/50A6L, G06Q40/06, G06Q40/04, G06Q40/00|
|May 18, 2007||AS||Assignment|
Owner name: MORGAN STANLEY, NEW YORK
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:ZBOROVSKIY, MIKHAIL;TURCHIN, DIMITRI;REEL/FRAME:019314/0905
Effective date: 20070514
Owner name: MORGAN STANLEY,NEW YORK
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:ZBOROVSKIY, MIKHAIL;TURCHIN, DIMITRI;REEL/FRAME:019314/0905
Effective date: 20070514
|Dec 9, 2013||FPAY||Fee payment|
Year of fee payment: 4